A family selects two phones from a box containing cellphones: four are Nokia, ma

Question

A family selects two phones from a box containing cellphones: four are Nokia, marked N1, N2, N3, and N4. The other three are Samsung, marked S1, S2, and S3. Two phones are picked randomly in succession without replacement. a) Express the following events as unions of the outcomes (1) One Nokia and One Samsung (2) Both are Nokia (3) Both are Samsung (4) Both are of the same kind b) Determine the probability that each of the following is true - the second pick is a Nokia, given that the first pick is a Samsung - the second pick is a Nokia, given that the first pick is also a Nokia

Explanation / Answer

a)

1) E = (First phone is Nokia AND Second Phone is Samsung) UNION (First phone is Samsung AND Second Phone isNokia ). = (N1S1UN1S2UN1S3UN2S1UN2S2UN3S3UN3S1UN3S2UN3S3UN4S1UN4S2UN4S3 ) U (S1N1 U S1N2 U S1N3 U S1N4 U S2N1 U S2N2 U S2N3 U S2N4 U S3N1 U S3N2 U S3N3 U S3N4)

2) E = First phone is Nokia AND Second Phone is Nokia = N1N2 UN1N3 UN1N4 U N2N1 U N2N3 U N2N4 U N3N1 U N3N2 U N3N4 U N4N1 U N4N2 U N4N3

3) S1S2U S1S3U S2S1U S2S3U S3S1U S3S2

4) (S1S2U S1S3U S2S1U S2S3U S3S1U S3S2) U (N1N2 UN1N3 UN1N4 U N2N1 U N2N3 U N2N4 U N3N1 U N3N2 U N3N4 U N4N1 U N4N2 U N4N3)

b)

1) first pick samsung, P = 1/4 (1 should be picked out of 4 remaining nokia)

2) first pick nokia P = 1/3 (1 should be picked out of 3 remaining nokia)

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