Answer:
When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen. Here the card is chosen with replacement. This implies probability for choosing a prime number remains the same as the previously drawn card is replaced.
The sample space= {1,2,3,4,5,6,7,8,9,10}
Prime numbers = {2,3,5,7}
Prob for drawing prime number = 4/10 = 0.4
is the same when replacement is done.
Also there are two outcomes either prime or non prime. Hence in this case, X the no of times a prime number is chosen, is binomial with p =0.4 and q = 0.6 and n=5
When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.
Prob for an even number = 0.5
But after one card drawn say odd number next card has prob for even number as 5/9 hence each draw is not independent of the other. Hence not binomial.
When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.
Here since every time replacement is done, probability of drawing a 3 remains constant = 1/10 = 0.3
i.e. each draw is independent of the other and there are only two outcomes , 3 or non 3. Hence here X is binomial.
When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen
Here X is the number of times a card is chosen with replacement till 5 is chosen. This is not binomial. Here probability for drawing nth time correct 5 is P(non 5 in the first n-1 draws)*P(5 in nth draw) = 0.1^(n-1) (0.9)
Because nCr is not appearing i.e. 5 cannot appear in any order but only in the last draw, this is not binomial.
Step-by-step explanation:
42789 times 54678
is 2,339,616,942
Show Work:
<span>Calculate 9 x 8, which is 72.
Since 72 is two-digit, we carry the first digit 7 to the next column.
</span>
3 <span>Calculate 8 x 8, which is 64. Now add the carry digit of 7, which is 71.
Since 71 is two-digit, we carry the first digit 7 to the next column.
</span>
4 <span>Calculate 7 x 8, which is 56. Now add the carry digit of 7, which is 63.
Since 63 is two-digit, we carry the first digit 6 to the next column.
</span>
5 <span>Calculate 2 x 8, which is 16. Now add the carry digit of 6, which is 22.
Since 22 is two-digit, we carry the first digit 2 to the next column.
</span>
6 <span>Calculate 4 x 8, which is 32. Now add the carry digit of 2, which is 34.
Since 34 is two-digit, we carry the first digit 3 to the next column.
</span>
7 <span>Bring down the carry digit of 3.
</span>
8 <span>Calculate 9 x 7, which is 63.
Since 63 is two-digit, we carry the first digit 6 to the next column.
</span>
9 <span>Calculate 8 x 7, which is 56. Now add the carry digit of 6, which is 62.
Since 62 is two-digit, we carry the first digit 6 to the next column.
</span>
10 <span>Calculate 7 x 7, which is 49. Now add the carry digit of 6, which is 55.
Since 55 is two-digit, we carry the first digit 5 to the next column.
</span>
11 <span>Calculate 2 x 7, which is 14. Now add the carry digit of 5, which is 19.
Since 19 is two-digit, we carry the first digit 1 to the next column.
</span>
12 <span>Calculate 4 x 7, which is 28. Now add the carry digit of 1, which is 29.
Since 29 is two-digit, we carry the first digit 2 to the next column.
</span>
13 <span>Bring down the carry digit of 2.
</span>
14 <span>Calculate 9 x 6, which is 54.
Since 54 is two-digit, we carry the first digit 5 to the next column.
</span>
15 <span>Calculate 8 x 6, which is 48. Now add the carry digit of 5, which is 53.
Since 53 is two-digit, we carry the first digit 5 to the next column.
</span>
16 <span>Calculate 7 x 6, which is 42. Now add the carry digit of 5, which is 47.
Since 47 is two-digit, we carry the first digit 4 to the next column.
</span>
17 <span>Calculate 2 x 6, which is 12. Now add the carry digit of 4, which is 16.
Since 16 is two-digit, we carry the first digit 1 to the next column.
</span>
18 <span>Calculate 4 x 6, which is 24. Now add the carry digit of 1, which is 25.
Since 25 is two-digit, we carry the first digit 2 to the next column.
</span>
19 <span>Bring down the carry digit of 2.
</span>
20 <span>Calculate 9 x 4, which is 36.
Since 36 is two-digit, we carry the first digit 3 to the next column.
</span>
21 <span>Calculate 8 x 4, which is 32. Now add the carry digit of 3, which is 35.
Since 35 is two-digit, we carry the first digit 3 to the next column.
</span>
22 <span>Calculate 7 x 4, which is 28. Now add the carry digit of 3, which is 31.
Since 31 is two-digit, we carry the first digit 3 to the next column.
</span>
23 <span>Calculate 2 x 4, which is 8. Now add the carry digit of 3, which is 11.
Since 11 is two-digit, we carry the first digit 1 to the next column.
</span>
24 <span>Calculate 4 x 4, which is 16. Now add the carry digit of 1, which is 17.
Since 17 is two-digit, we carry the first digit 1 to the next column.
</span>
25 <span>Bring down the carry digit of 1.
</span>
26 <span>Calculate 9 x 5, which is 45.
Since 45 is two-digit, we carry the first digit 4 to the next column.
</span>
27 <span>Calculate 8 x 5, which is 40. Now add the carry digit of 4, which is 44.
Since 44 is two-digit, we carry the first digit 4 to the next column.
</span>
28 <span>Calculate 7 x 5, which is 35. Now add the carry digit of 4, which is 39.
Since 39 is two-digit, we carry the first digit 3 to the next column.
</span>
29 <span>Calculate 2 x 5, which is 10. Now add the carry digit of 3, which is 13.
Since 13 is two-digit, we carry the first digit 1 to the next column.
</span>
30 <span>Calculate 4 x 5, which is 20. Now add the carry digit of 1, which is 21.
Since 21 is two-digit, we carry the first digit 2 to the next column.
</span>
31 <span>Bring down the carry digit of 2.
</span>
32 <span>Calculate 342312 + 2995230 + 25673400 + 171156000 + 2139450000, which is 2339616942</span>
<span> </span>
-2* F
You do +3 +2 -4 -1 which equals to 0. Then you do 0 plus -2 which equals -2*F.
