A basketball player for a regular season had a free-throwsuccess probability of

Question

A basketball player for a regular season had a free-throwsuccess probability of 0.6. Determine the likelihood that he/shewould have to shoot 7 times to make a first basket (scoring apoint).
Note: the answer should have 5 significant digitsafter the decimal point.

A basketball player for a regular season had a free-throwsuccess probability of 0.6. Determine the likelihood that he/shewould have to shoot 7 times to make a first basket (scoring apoint).
Note: the answer should have 5 significant digitsafter the decimal point.

Explanation / Answer

Since we're assuming that the outcome of each free-throw israndom and that the free-throws are not affected by the throwspreceding them, each subsequent free throw also has a probabilityof success of 0.6.
As you probably know, the probability of two independentevents A and B both occurring is PA* PB, inwhich PA = probability of Aand PB= probability of B.
Now on to your problem:
The probability that the player misses the first free throw is0.4. The probability that the player misses the first AND secondfree throw is 0.4*0.4. The probability that the player misses the first, second ANDthird free throw is 0.4*0.4*0.4. ... The probability that the player misses 6 times in a row is0.46. Finally, the probability that the player misses 6 free throwsin a row and then makes the 7th shotis 0.46*0.6.
0.46*0.6 = 0.004096 * 0.6= 0.0024576
The answer should have 5 significant digits after the decimalpoint. However, zeros to the left on non-zero digits are notsignificant, as they simply serve to locate the decimal point.Therefore, the final answeris 0.0024576.
I hope I helped!

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