mary shots free throws 70% on average. She is fouled shooting a three point shot and therefore gets 3 free throws. What is the probability she:
*makes first misses seconds and third shots
*Makes at least 1 shot
h -- hit
m -- miss
she has the following cases:
hhh
hhm
hmh
mhh
hmm *
mhm
mmh
mmm
"makes first misses seconds and third shots " --- I see one case, marked with *
so prob(hmm) = 1/8
"Makes at least 1 shot"
all except mmm
so prob(of that event) = 1 - 1/8 = 7/8
ignore my previous answers, I totally forgot about the actual probabilities.
so for
prob(makes first misses seconds and third shots)
= (7/10)(3/10)(3/10)
= 63/1000 or .063
prob(missing all 3) = (3/10)^3 = 27/1000
so prob(of making at least one shot)
= 1 - 27/1000
= 973/1000
= .973
To determine the probability of Mary making the first shot, missing the second, and then making the third shot, we need to multiply the probabilities of each event occurring.
1. Probability of making the first shot:
Since Mary has a 70% average accuracy, the probability of her making the first shot is 70% or 0.70.
2. Probability of missing the second shot:
As she has already made the first shot, there are only two possible outcomes for the second shot: make or miss. Since she made the first shot and has a 70% average accuracy, the probability of missing the second shot is 100% - 70% = 30% or 0.30.
3. Probability of making the third shot:
Again, since she has already made the first shot, there are two possible outcomes for the third shot: make or miss. Given her 70% average accuracy, the probability of making the third shot is 70% or 0.70.
To calculate the overall probability of this specific sequence, we multiply the probabilities together:
0.70 * 0.30 * 0.70 = 0.147 (approximately)
So, the probability of Mary making the first shot, missing the second shot, and then making the third shot is approximately 0.147 or 14.7%.
To calculate the probability of Mary making at least 1 shot, we can use the complement rule. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
In this case, the event of Mary making at least 1 shot is the complement of the event of her missing all 3 shots.
1. Probability of missing a single shot:
The probability of Mary missing a single shot is 1 - 0.70 = 0.30.
2. Probability of missing all 3 shots:
Since there are 3 shots in total, and the probability of missing a single shot is 0.30, the probability of missing all 3 shots can be calculated by multiplying the probabilities together:
0.30 * 0.30 * 0.30 = 0.027 (approximately)
3. Probability of making at least 1 shot:
Now, we can apply the complement rule to get the probability of Mary making at least 1 shot:
1 - 0.027 = 0.973 (approximately)
Therefore, the probability of Mary making at least 1 shot is approximately 0.973 or 97.3%.