A psychology experiment on memory was conducted which required participants to note which songs they found...

A psychology experiment on memory was conducted which required participants to note which songs they found pleasing. Based on many results, the (partial) probability distribution below was determined for the discrete random variable X = number of songs found pleasing (during a fixed time period).

X = # songs	1	2	3	4	5	6	7	8	9	10
Probability	0	0.02	0.04	0.07	0.15	0.18	0.24	0.14	0.11	0.05

Given that the person finds at least 7 songs pleasing to the ear, what is the probability that they find 8 songs pleasing to the ear? Please round to the second decimal point.

Expert Solution

To find P(X = 8/ X Greater than or equal to 7):

By Multiplication Theorem of Probability:

P(X = 8/ X Greater than or equal to 7) = P(X = 8 AND X Greater than or equal to 7) / P(X Greater than or equal to 7)

= (P(X=8)+P(X=9)+P(X=10))/P(X Greater than or equal to 7)

= ( 0.14+0.11+0.05)/(0.24+0.14+0.11+0.05)

= 0.30/0.54

= 0.5556

So,

Answer is:

0.5556

orchestra answered 1 year ago

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