Question

The numbers 1 to 40 are marked on ping-pong balls and put into a
barrel. If a ball is drawn at random, find:
(i) P(multiple of 4) (ii) P(multiple of 7)
(iii) P(multiple of 28) (iv) P(multiple of 4 or 7).
(b) Are the events ‘drawing a multiple of 4’ and ‘drawing a multiple of 7’
independent? Explain. I just need help with the last question - B - but I thought the other information would be useful.

Answer 1

there are 40 balls in all..
since there are 10 numbers between 1 and 40 inclusive that are multiples of 4,
P(mult4) = 10/40 = 1/4
since there are 5 numbers between 1 and 40 inclusive that are multiplse of 7,
P(mult7) = 7/40
since there is only 1 number between 1 and 40.. blah. blah blah.,
P(mult28) = 1/40
since there are 10 #s mult of 4 and 7 #s mult 7 and since 28 is both a member of mult4 and mult7, you only need to count that once... so
P(mult4 or mult7) = 16/40 = 2/5