Alice solves every puzzle with probability 0.6 , and Bob, with probability 0.5 . They are given 7 puzzles and each chooses 5 out of the 7 puzzles randomly and solves them independently. A puzzle is considered solved if at least one of them solves it. What is the probability that all the 7 puzzles happen to be solved by at least one of them

0.021943

Step-by-step explanation:

Alice solves every puzzle with a probability of  0.6

Bob solves every puzzle with a probability of 0.5

Number of puzzles given = 7

The probability of a puzzle been solved by either Alice or Bob

P = P( A U B ) = P( A ) + P( B ) - P( A n B )

                      =  0.6 + 0.5 - ( 0.6 * 0.5 )  = 0.8

probability of all 7 puzzles solved = (P( A ))^2 * ( P )^3 * (p(B))^2

                                                        = ( 0.6 )^2 * (0.8)^3 * (0.5)^2 = 0.04608

Finally determine the P ( choosing 5 out of 7 for both such that all the 7 are chosen )

attached below is the remaining part of the solution

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm