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 Second set Red 0.6 Not red Red 0.7 Not red Not red 0.2 Not red (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 Probability: 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.

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Answer

The tree diagram is completed by filling in the probabilities for the second set of traffic lights. The probability for the first set being not red is:

egin{align*} P( ext{Not red}) &= 1 - P( ext{Red})
&= 1 - 0.6
&= 0.4 ext{For the second set:} P( ext{Not red}) &= 1 - P( ext{Red})
&= 1 - 0.7
&= 0.3

Final tree diagram probabilities are:

First Set: Red: 0.6, Not Red: 0.4
Second Set: Red: 0.7, Not Red: 0.3

Step 2

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

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Answer

The probability that the first set is not red is:

$P( ext{Not red}) = 0.4$ .

Step 3

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

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Answer

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

$P( ext{Not red | Red}) = 0.3$ .

Step 4

Work out the probability that both sets are not red.

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Answer

To find the probability that both sets are not red, we use:

$P( ext{Both not red}) = P( ext{Not red}) imes P( ext{Not red}) = 0.4 imes 0.3 = 0.12$ .

Step 5

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

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Answer

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

$P( ext{At least one red}) = 1 - P( ext{Both not red})$

$= 1 - 0.12 = 0.88$ .

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.

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