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The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62 - OCR - GCSE Maths - Question 7 - 2018 - Paper 6

Question 7

The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62. The probability that any postcard posted in Portugal o... show full transcript

Worked Solution & Example Answer:The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62 - OCR - GCSE Maths - Question 7 - 2018 - Paper 6

Step 1

How many of her postcards can she expect to be delivered within a week?

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Answer

To determine how many postcards Anna can expect to have delivered within a week, we can use the formula for expected value:

$E(X) = n imes p$

Where:

$n$ is the total number of postcards (15)
$p$ is the probability of delivery within a week (0.62)

Calculating this gives:

$E(X) = 15 imes 0.62 = 9.3$

Since the expected number of postcards delivered cannot be fractional, we round this to the nearest whole number. Therefore, Anna can expect 9 postcards to be delivered within a week.

Step 2

Complete the probability tree to show the possible outcomes for the postcards.

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Answer

The probability tree can be completed as follows:

Monday's postcard:
- Delivered within a week (Probability = 0.62)
- Not delivered within a week (Probability = 1 - 0.62 = 0.38)
Friday's postcard:
- Delivered within a week (Probability = 0.41)
- Not delivered within a week (Probability = 1 - 0.41 = 0.59)

This results in the following probabilities:

Monday's postcard delivered: 0.62
- Friday's postcard delivered: 0.41
- Friday's postcard not delivered: 0.59
Monday's postcard not delivered: 0.38
- Friday's postcard delivered: 0.41
- Friday's postcard not delivered: 0.59

Step 3

Calculate the probability that only one of Sergio's postcards is delivered within a week.

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Answer

To calculate the probability that only one of Sergio's postcards is delivered within a week, we can examine the two cases:

Monday's postcard is delivered, and Friday's postcard is not delivered:
- Probability = $0.62 imes 0.59 = 0.3658$
Monday's postcard is not delivered, and Friday's postcard is delivered:
- Probability = $0.38 imes 0.41 = 0.1558$

Now, we sum these two probabilities:

$P( ext{Only one delivered}) = 0.3658 + 0.1558 = 0.5216$

Thus, the probability that only one postcard is delivered within a week is 0.5216.

The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62 - OCR - GCSE Maths - Question 7 - 2018 - Paper 6

Worked Solution & Example Answer:The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62 - OCR - GCSE Maths - Question 7 - 2018 - Paper 6

How many of her postcards can she expect to be delivered within a week?

Complete the probability tree to show the possible outcomes for the postcards.

Calculate the probability that only one of Sergio's postcards is delivered within a week.

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