Question

The probability of winning on a slot machine is 3%. If the slot machine is played 200 times, find the probability of winning 5 times. Use a TI-83, TI-83 Plus, or TI-84 calculator to find the probability. a) 0.0625 b) 0.1354 c) 0.0002 d) 0.2147

Answer 1

To find the probability of winning 5 times out of 200 plays on a slot machine with a 3% chance of winning each time, use the binomial probability formula. The correct answer is d) 0.2147.

Step-by-step explanation:

To find the probability of winning 5 times out of 200 plays on a slot machine with a 3% chance of winning each time, we can use the binomial probability formula. The formula is:

P(x) = combination(n, x) * p^x * (1-p)^(n-x)

Where:

• P(x) is the probability of getting exactly x successes
• n is the number of trials (in this case, 200 plays)
• p is the probability of success on each trial (in this case, 0.03)
• x is the number of desired successes (in this case, 5)

Using a calculator like the TI-83, TI-83 Plus, or TI-84, we can calculate:

P(5) = combination(200, 5) * 0.03^5 * (1-0.03)^(200-5)

This gives us the probability of winning 5 times out of 200 plays. Comparing the options given, the correct answer is d) 0.2147.

Answer 2

The probability of winning 5 times out of 200 plays on a slot machine with a 3% probability of winning, use the binomial probability formula. The result is approximately 0.0625.

The probability of winning 5 times out of 200 plays on a slot machine with a 3% probability of winning, you can use the binomial probability formula. The formula is:

P(X=k) = C(n,k) ·
`p^k` ·
`(1-p)^(n-k)`

where:

n is the number of trials (plays)

k is the number of successes (wins)

p is the probability of winning on a single play

C(n,k) is the number of ways to choose k successes out of n trials

In this case:

n = 200, k = 5, p = 0.03

P(X=5) = C(200,5) ·
`(0.03)^5` ·
`(1-0.03)^(195)`

You can use the binomial probability function on your TI-83, TI-83 Plus, or TI-84 calculator to compute this. Make sure to use the combination function (usually denoted as nCr or C(n,k)) on your calculator.

The result is approximately 0.0625, so the correct answer is option a) 0.0625.