Photo AI

The success rate of the Fana soccer team depends on a number of factors - NSC Mathematics - Question 11 - 2017 - Paper 1

Question icon

Question 11

The-success-rate-of-the-Fana-soccer-team-depends-on-a-number-of-factors-NSC Mathematics-Question 11-2017-Paper 1.png

The success rate of the Fana soccer team depends on a number of factors. The fitness of the players is one of the factors that influence the outcome of a match. - T... show full transcript

Worked Solution & Example Answer:The success rate of the Fana soccer team depends on a number of factors - NSC Mathematics - Question 11 - 2017 - Paper 1

Step 1

The probability that all the players are fit for the next match is 70%

96%

114 rated

Answer

Given that the probability of all players being fit is P(F)=0.7P(F) = 0.7.

Step 2

If all the players are fit to play the next match, the probability of winning the next match is 85%

99%

104 rated

Answer

The winning probability given that all are fit is P(W∣F)=0.85P(W|F) = 0.85.

Step 3

If there are players that are not fit to play the next match, the probability of winning the match is 55%

96%

101 rated

Answer

The winning probability given that not all are fit is P(W∣notF)=0.55P(W|not F) = 0.55.

Step 4

Calculate the probability that the Fana soccer team will win the next match.

98%

120 rated

Answer

To find the total probability of winning, use the law of total probability:

P(Win)=P(F)×P(W∣F)+P(notF)×P(W∣notF)P(Win) = P(F) \times P(W|F) + P(not F) \times P(W|not F)

Since P(notF)=1−P(F)=0.3P(not F) = 1 - P(F) = 0.3, we can substitute:

P(Win)=0.7×0.85+0.3×0.55P(Win) = 0.7 \times 0.85 + 0.3 \times 0.55

Calculating these gives:

P(Win)=0.595+0.165=0.76P(Win) = 0.595 + 0.165 = 0.76

Thus, the probability that they will win the match is 76%.

Join the NSC students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;