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Over [174]
3 years ago
13

4. Assume that the chances of a basketball player hitting a 3-pointer shot is 0.4 and the probability of hitting a free-throw is

0.65. Assume that in a given game the player shoots 10 free throws and 10 3-point shots. Treat each shot is an independent trial and calculate the probability that the player will make exactly 3 3-pointers and 5-free throws.
Mathematics
1 answer:
vovikov84 [41]3 years ago
5 0

Answer:

0.0334 = 3.34% probability that the player will make exactly 3 3-pointers and 5-free throws.

Step-by-step explanation:

For each 3-pointer shot, there are only two possible outcomes. Either the player makes it, or the player does not. The same is valid for free throws. This means that both the number of 3-pointers and free throws made are given by binomial distributions.

Since 3-pointers and free throws are independent, first we find the probability of making exactly 3 3-pointers out of 10, then the probability of making exactly 5 free throws out of 10, and then the probability that the player will make exactly 3 3-pointers and 5-free throws is the multiplication of these probabilities.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Probability of making 3 3-pointers out of 10:

The chances of a basketball player hitting a 3-pointer shot is 0.4, which means that p = 0.4. So this is P(X = 3) when n = 10.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.21499

Probability of making 5 free throws out of 10:

The probability of hitting a free-throw is 0.65, which means that p = 0.65. The probability is P(X = 5) when n = 10.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{10,5}.(0.65)^{5}.(0.35)^{5} = 0.15357

Calculate the probability that the player will make exactly 3 3-pointers and 5-free throws.

0.21499*0.15537 = 0.0334

0.0334 = 3.34% probability that the player will make exactly 3 3-pointers and 5-free throws.

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Using only four 4's and any operational sign find the value of 8
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Answer:

The answer is 4 + 4 + 4 - 4 = 8

Step-by-step explanation:

The four fours problem is one of the problems given in the book "The Man Who Calculated" by Malba Tahan, a Brazilian-born professor of mathematical sciences.

There are many complicated problems in this book made with the intention of using logic to find a value.

The 4 fours problem is based on using these numbers and using any operation to result in the numbers 1 through 10.

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3 years ago
Using Cavalieri's Principle, what is the general formula for the volume of a cone?
Anit [1.1K]

Answer:

The volume for a cone and pyramid are the same, V = 1/3 Bh where B is the area of the base.

Step-by-step explanation:

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4 0
2 years ago
A bag contains 4 white,5 blacks and 2 blue balls. 3 balls are drawn one after the other without replacement from the bag .what i
Doss [256]

Answer:

24/99

Step-by-step explanation:

From the question given above, the following data were obtained:

White (W) balls = 4

Black (B) balls = 5

Blue (Bl) balls = 2

Probability that they are of different color =?

Next, we shall determine the total number of balls in the bag. This can be obtained as follow:

White (W) balls = 4

Black (B) balls = 5

Blue (Bl) balls = 2

TOTAL = 4 + 5 + 2 = 11 balls

Next, we shall determine the possible outcome of draw. This can be obtained as follow.

The possible outcome could be:

WBLB or WBBL or BBLW or BWBL or BLBW or BLWB

Next we shall determine the probability of each of outcomes.

Since the ball is drawn without replacement, it means the total number of ball will reduce after each draw.

White (W) balls = 4

Black (B) balls = 5

Blue (Bl) balls = 2

TOTAL = 11

P(WBLB) = 4/11 × 2/10 × 5/9 = 40/990

P(WBLB) = 4/99

P(WBBL) = 4/11 × 5/10 × 2/9 = 40/990

P(WBBL) = 4/99

P(BBLW) = 5/11 × 2/10 × 4/9 = 40/990

P(BBLW) = 4/99

P(BWBL) = 5/11 × 4/10 × 2/9 = 40/990

P(BWBL) = 4/99

P(BLBW) = 2/11 × 5/10 × 4/9 = 40/990

P(BLBW) = 4/99

P(BLWB) = 2/11 × 4/10 × 5/9 = 40/990

P(BLWB) = 4/99

Finally, we shall determine the probability that they are of different color. This can be obtained as follow:

P(WBLB) = 4/99

P(WBBL) = 4/99

P(BBLW) = 4/99

P(BWBL) = 4/99

P(BLBW) = 4/99

P(BLWB) = 4/99

Probability that they are of different color =?

Probability that they are of different color = P(WBLB) + P(WBBL) + P(BBLW) + P(BWBL) + P(BLBW) + P(BLWB)

= 4/99 + 4/99 + 4/99 + 4/99 + 4/99 + 4/99

= (4 + 4 + 4 + 4 + 4 + 4)/99

= 24/99

Thus, the probability that they are of different color is 24/99

4 0
3 years ago
Need help what’s 7-11??
nydimaria [60]

Answer:

umm the answer to 7-11 is 69

Step-by-step explanation:

7. Always

8. sometimes

9. never

10. never

11. always

6 0
3 years ago
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