Answer:
(a) 7.69%
(b) 25%
(c) 2.78%
Step-by-step explanation:
(a)
In a deck of 52 cards there are 4 aces.
The odds in favor or the probability of selecting an ace is:
![P(Ace) = \frac{Number\ of\ aces}{Number\ of\ cards\ in\ total}\\ =\frac{4}{52}\\ =0.076923\\\approx7.69\%](https://tex.z-dn.net/?f=P%28Ace%29%20%3D%20%5Cfrac%7BNumber%5C%20of%5C%20aces%7D%7BNumber%5C%20of%5C%20cards%5C%20in%5C%20total%7D%5C%5C%20%3D%5Cfrac%7B4%7D%7B52%7D%5C%5C%20%3D0.076923%5C%5C%5Capprox7.69%5C%25)
Thus, the probability of selecting an ace from a random deck of 562 cards is 7.69%.
(b)
The outcomes of each toss of a coin is independent of the other, since the result of the previous toss does not affect the result of the current toss.
The probability that both the tosses will end up in heads is:
![P(2\ Heads)=P(1^{st}\ Head)\times P(2^{nd}\ Head)\\=\frac{1}{2}\times \frac{1}{2}\\ =\frac{1}{4}\\ =0.25\ or\ 25\%\\](https://tex.z-dn.net/?f=P%282%5C%20Heads%29%3DP%281%5E%7Bst%7D%5C%20Head%29%5Ctimes%20P%282%5E%7Bnd%7D%5C%20Head%29%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%20%3D%5Cfrac%7B1%7D%7B4%7D%5C%5C%20%3D0.25%5C%20or%5C%2025%5C%25%5C%5C)
Thus, the probability that both the tosses will end up in heads is 25%.
(c)
The sample space of two dice consists of 36 outcomes in total.
Out of these 36 outcomes there is only 1 Boxcar, i.e. two sixes.
The probability of a boxcar when two dice are rolled is:
![P(Boxcar)=\frac{Favorable\ outcomes}{Total\ no.\ of\ outcomes}\\= \frac{1}{36}\\ =0.027777\\\approx2.78\%](https://tex.z-dn.net/?f=P%28Boxcar%29%3D%5Cfrac%7BFavorable%5C%20outcomes%7D%7BTotal%5C%20no.%5C%20of%5C%20outcomes%7D%5C%5C%3D%20%5Cfrac%7B1%7D%7B36%7D%5C%5C%20%3D0.027777%5C%5C%5Capprox2.78%5C%25)
Thus, the probability of a boxcar when two dice are rolled is 2.78%.
Answer:
6 x 7 is 42, so A m a y b e?
Step-by-step explanation:
Answer:
The angles in the diagram add up to 90°
To find x add the two angles and equate them to 90°
That's
8x + 50 = 90
8x = 90-50
8x = 40
Divide both sides by 8
8x/8 = 40/8
x = 5
Hope this helps you
Answer:
w= -1
Step-by-step explanation:
Use PEMDAS to solve.
9(1 + w) - 5w = 5
distribute 9 to everything inside the parentheses.
9 x 1 = 9
9 x w = 9w
rewrite equation
9 + 9w - 5w = 5
combine like terms
9w - 5w = 4w
rewrite equation
9 + 4w = 5
subtract 9 from both sides
9 - 9 = 0
5 - 9 = -4
rewrite equation
4w = -4
divide by 4 on both sides to get w by itself.
4w / 4 = w
-4 / 4 = -1
<u>Hope This Helps :)</u>