Hi Can someone please help me with the problem below.
When Bill bowls, he can get a strick 60% of the time. How many times more likely is it for Bill to bowl at least three strikes out of four tries as it is for him to bowl zero strikes out of four tries. Round to nearest whole number.
I gpt 47 times more likely. Is that correct.
To solve this problem, we need to calculate the probabilities of two events: (1) Bill bowling at least three strikes out of four tries, and (2) Bill bowling zero strikes out of four tries. Let's break it down step by step:
Event 1: Bill bowling at least three strikes out of four tries.
To calculate this probability, we need to consider all the possible combinations of strikes and non-strikes in four attempts and calculate the probability for each scenario:
1. Bill gets four strikes: Probability = 0.6 * 0.6 * 0.6 * 0.6 = 0.6^4.
2. Bill gets three strikes and one non-strike: Probability = 0.6 * 0.6 * 0.6 * 0.4 = 0.6^3 * 0.4 * 4 (since there are four possible positions for the non-strike).
3. Bill gets two strikes and two non-strikes: Probability = 0.6 * 0.6 * 0.4 * 0.4 = 0.6^2 * 0.4^2 * 6 (since there are six possible combinations for two strikes and two non-strikes).
4. Bill gets one strike and three non-strikes: Probability = 0.6 * 0.4 * 0.4 * 0.4 = 0.6 * 0.4^3 * 4 (since there are four possible positions for the strike).
5. Bill gets zero strikes and four non-strikes: Probability = 0.4 * 0.4 * 0.4 * 0.4 = 0.4^4.
Now, we can calculate the overall probability of Bill bowling at least three strikes:
P(at least three strikes) = Probability(1) + Probability(2) + Probability(3) + Probability(4) = 0.6^4 + 0.6^3 * 0.4 * 4 + 0.6^2 * 0.4^2 * 6 + 0.6 * 0.4^3 * 4.
Event 2: Bill bowling zero strikes out of four tries.
P(zero strikes) = Probability(5) = 0.4^4.
Now, let's calculate the ratio between the two probabilities:
Ratio = P(at least three strikes) / P(zero strikes).
By substituting the values into the formula, we can determine the numerical value of this ratio. After calculating the ratio, round it to the nearest whole number.
Therefore, the next step would be to calculate the ratio and check if your answer matches the value of 47.