Rashid drives his car along a road passing through two sets of traffic lights. The tree diagram shows the probabilities of the lights being red when he reaches them. First set | Red | 0.6 | | Not red | 0.4 | Second set | Red | 0.7 | | Not red | 0.2 | (a) Complete the tree diagram. (b) Write down the probability that the first set is not red. (c) Given that the first set is red, write down the probability that the second set is not red. (d) Work out the probability that both sets are not red. (e) Work out the probability that at least one set is red.

GCSE OCR Maths Tree diagrams: Rashid drives his car along a ro

Rashid drives his car along a road passing through two sets of traffic lights - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Question 13

Rashid drives his car along a road passing through two sets of traffic lights. The tree diagram shows the probabilities of the lights being red when he reaches them... show full transcript

Worked Solution & Example Answer:Rashid drives his car along a road passing through two sets of traffic lights - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Step 1

Complete the tree diagram.

96%

114 rated

Answer

To complete the tree diagram, we need to fill in the probabilities for the second set of lights.

For the first set, we have the following probabilities:

Probability of Red: 0.6
Probability of Not Red: 0.4 (which is 1 - 0.6)

For the second set (where the probabilities are given):

If the first set is Red, the probability of the second set being Red is 0.7, and Not Red is therefore 0.3 (1 - 0.7).
If the first set is Not Red, the probability of the second set being Red remains 0.2, and Not Red is 0.8 (1 - 0.2).

Thus, the completed tree diagram looks like this:

First Set: Red (0.6) -> Second Set: Red (0.7) & Not Red (0.3)
First Set: Not Red (0.4) -> Second Set: Red (0.2) & Not Red (0.8)

Step 2

Write down the probability that the first set is not red.

99%

104 rated

Answer

The probability that the first set is not red is given directly in the tree diagram:

$P(\text{Not Red}) = 0.4$

Step 3

Given that the first set is red, write down the probability that the second set is not red.

96%

101 rated

Answer

Given that the first set is red, the probability that the second set is not red is:

$P(\text{Not Red | Red}) = 0.3$

Step 4

Work out the probability that both sets are not red.

98%

120 rated

Answer

To find the probability that both sets are not red:

The probability of the first set being not red is 0.4.
If the first set is not red, the probability of the second set being not red is 0.8.

Using the multiplication rule for independent events:

$P(\text{Both Not Red}) = P(\text{1st Not Red}) \times P(\text{2nd Not Red | 1st Not Red}) = 0.4 \times 0.8 = 0.32$

Step 5

Work out the probability that at least one set is red.

97%

117 rated

Answer

To find the probability that at least one set is red, we can use the complement rule:

Calculate the probability of both sets being not red (which we found as 0.32).
The probability that at least one set is red is:

$P(\text{At least one Red}) = 1 - P(\text{Both Not Red}) = 1 - 0.32 = 0.68$

Rashid drives his car along a road passing through two sets of traffic lights - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Worked Solution & Example Answer:Rashid drives his car along a road passing through two sets of traffic lights - OCR - GCSE Maths - Question 13 - 2017 - Paper 1

Complete the tree diagram.

Write down the probability that the first set is not red.

Given that the first set is red, write down the probability that the second set is not red.

Work out the probability that both sets are not red.

Work out the probability that at least one set is red.

Join the GCSE students using SimpleStudy...