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# When Matthew plays his favorite golf course, his probability of making

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
When Matthew plays his favorite golf course, his probability of making  [#permalink]

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08 Nov 2019, 01:48
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Difficulty:

35% (medium)

Question Stats:

64% (01:47) correct 36% (01:55) wrong based on 42 sessions

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Competition Mode Question

When Matthew plays his favorite golf course, his probability of making a par or better on a par-3 hole is .3. If Matthew is playing his favorite golf course, and that course has exactly 4 par-3 holes, what is the probability that Matthew will make par or better on at least one of the par-3 holes?

A. 0.0081
B. 0.2401
C. 0.3000
D. 0.7599
E. 0.9919

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Re: When Matthew plays his favorite golf course, his probability of making  [#permalink]

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08 Nov 2019, 02:36
1
Let the probability of making a par or better on a par-3 hole = A = 0.3
& probability of NOT making a par or better on a par-3 hole = B = 1 - 0.3 = 0.7

Of Exactly 4 par-3 holes, Probability that Matthew will make par or better on at least one of the par-3 holes
= 1 - Probability (Exactly NO par-3 holes)
= $$1 - 4C_0*(0.7)^4$$
= $$1 - 1*0.2401$$
= $$0.7599$$

IMO Option D
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Re: When Matthew plays his favorite golf course, his probability of making  [#permalink]

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08 Nov 2019, 03:57
1
not getting into par -3 = .7
so for 4 chances we get .7^4 = .2401
1-.2401 ; .7599 at least one of the par-3 holes
IMO D

When Matthew plays his favorite golf course, his probability of making a par or better on a par-3 hole is .3. If Matthew is playing his favorite golf course, and that course has exactly 4 par-3 holes, what is the probability that Matthew will make par or better on at least one of the par-3 holes?

A. 0.0081
B. 0.2401
C. 0.3000
D. 0.7599
E. 0.9919
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Posts: 1139
Location: United States
Re: When Matthew plays his favorite golf course, his probability of making  [#permalink]

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08 Nov 2019, 04:04
1
Quote:
When Matthew plays his favorite golf course, his probability of making a par or better on a par-3 hole is .3. If Matthew is playing his favorite golf course, and that course has exactly 4 par-3 holes, what is the probability that Matthew will make par or better on at least one of the par-3 holes?

A. 0.0081
B. 0.2401
C. 0.3000
D. 0.7599
E. 0.9919

1-P(NOT)=P(ATLEAST1)
P(NOT)=NNNN=(7/10)^4=2401/10,000
1-P(NOT)=10,000-2401/10,000=7599/10,000

Ans. (D)
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Re: When Matthew plays his favorite golf course, his probability of making  [#permalink]

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Updated on: 10 Nov 2019, 06:39
1
Probability of Matthew making par or better on a par-3 hole = 0.3.
Probality of not making a par or better =0.7
We are to determine the probability of Matthew making at least one par or better on a golf course that has exactly 4 par-3 holes.
Let P(none)= probability of Matthew not making par or better on any 4 par-3 holes and P(E)= probability of Matthew making par or better on at least one par-3 hole.
then P(E) = 1-P(none)
P(none)= 0.7^4= 0.2401
P(E)=1-0.2401 = 0.7599

The answer is, therefore, option D.

Originally posted by eakabuah on 08 Nov 2019, 09:27.
Last edited by eakabuah on 10 Nov 2019, 06:39, edited 2 times in total.
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Joined: 22 Feb 2018
Posts: 451
Re: When Matthew plays his favorite golf course, his probability of making  [#permalink]

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09 Nov 2019, 02:21
When Matthew plays his favorite golf course, his probability of making a par or better on a par-3 hole is .3. If Matthew is playing his favorite golf course, and that course has exactly 4 par-3 holes, what is the probability that Matthew will make par or better on at least one of the par-3 holes?

P (at least one of the par-3 holes) = Total probability - none = 1 - 0.7 = 0.3

Imo. C
Re: When Matthew plays his favorite golf course, his probability of making   [#permalink] 09 Nov 2019, 02:21
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