A darts team is going to play a match on Saturday and on Sunday. The probability that the team will win on Saturday is 0.45. If they win on Saturday, the probability that they will win on Sunday is 0.67. If they do not win on Saturday, the probability that they will win on Sunday is 0.35. (a) Complete the probability tree diagram. (b) Find the probability that the team will win exactly one of the two matches.

GCSE Edexcel Maths Coordinate Geometry: A darts team is going to play a

A darts team is going to play a match on Saturday and on Sunday - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 2

Question 16

A darts team is going to play a match on Saturday and on Sunday. The probability that the team will win on Saturday is 0.45. If they win on Saturday, the probabilit... show full transcript

Worked Solution & Example Answer:A darts team is going to play a match on Saturday and on Sunday - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 2

Step 1

Complete the probability tree diagram.

96%

114 rated

Answer

For the probability tree diagram:

On Saturday, the probability of winning is 0.45, and of not winning is 0.55.
If they win on Saturday, the probability of winning on Sunday is 0.67, and of not winning is 0.33.
If they do not win on Saturday, the probability of winning on Sunday is 0.35, and of not winning is 0.65.

Thus, the complete probabilities are:

Win on Saturday, Win on Sunday: $0.45 * 0.67 = 0.3015$ (approximately 0.30)
Win on Saturday, Not Win on Sunday: $0.45 * 0.33 = 0.1485$ (approximately 0.15)
Not Win on Saturday, Win on Sunday: $0.55 * 0.35 = 0.1925$ (approximately 0.19)
Not Win on Saturday, Not Win on Sunday: $0.55 * 0.65 = 0.3575$ (approximately 0.36)

Step 2

Find the probability that the team will win exactly one of the two matches.

99%

104 rated

Answer

To find the probability of winning exactly one match, we consider two scenarios:

Winning on Saturday and not winning on Sunday:
- Probability = $0.45 * 0.33 = 0.1485$
Not winning on Saturday and winning on Sunday:
- Probability = $0.55 * 0.35 = 0.1925$

Now, we add these two probabilities together to find the total probability of winning exactly one match:

$ext{Total Probability} = 0.1485 + 0.1925 = 0.341$

Thus, the probability that the team will win exactly one of the two matches is 0.341.

A darts team is going to play a match on Saturday and on Sunday - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 2

Worked Solution & Example Answer:A darts team is going to play a match on Saturday and on Sunday - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 2

Complete the probability tree diagram.

Find the probability that the team will win exactly one of the two matches.

Join the GCSE students using SimpleStudy...