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The probability that Sam works from home on Monday is 0.4 - OCR - GCSE Maths - Question 24 - 2023 - Paper 1

Question 24

The probability that Sam works from home on Monday is 0.4. The probability that Sam works from home on Friday is 0.2. (a) Complete the tree diagram. (b) Work out t... show full transcript

Worked Solution & Example Answer:The probability that Sam works from home on Monday is 0.4 - OCR - GCSE Maths - Question 24 - 2023 - Paper 1

Step 1

Complete the tree diagram.

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Answer

To complete the tree diagram, we need to add the complementary probabilities for each day. The probability that Sam does not work from home on Monday is:

$1 - 0.4 = 0.6$

For Friday, the probability that Sam does not work from home is:

$1 - 0.2 = 0.8$

Thus, the completed tree diagram should look like this:

          Monday
         /       \
       0.4        0.6
     Work from    Does not
     home         work from home
     /          \
   Friday       Friday
   /   \        /   \
0.2   0.8   0.2   0.8
Work    Does not   Work   Does not
from    work from  from   work from
home    home       home   home

Step 2

Work out the probability that Sam works from home on Monday but does not work from home on Friday.

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Answer

To find the probability that Sam works from home on Monday and does not work from home on Friday, we can use the multiplication rule of probability:

$P(A ext{ and } B) = P(A) imes P(B)$

In this case, let:

A = Sam works from home on Monday (0.4)
B = Sam does not work from home on Friday (0.8)

So we calculate:

$P(A ext{ and not } B) = P(A) imes P(B) = 0.4 imes 0.8 = 0.32$

Thus, the probability that Sam works from home on Monday but does not work from home on Friday is 0.32.

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