Question

6) Transport an lorries inpectors carry out roadside safety tests 1) The probability of a randomly selected lorry fondon failling the tests is 0.25. A transport Inspector chooses two Torries at randon find the probability that: i) Both will fail the test 11) Exactly one will pass the test. 2) Of 12 lorries parked outside a transport cafe, four would fail if tested. i) An inspector choses two of these twelve lorries at random find the probability that both will pass the test and one will fail the test. ii) An inspector chooses three of these lorries at randomly.tind the probability that two will pass the test and one will fail the test. in An inspector chooses four of these lorries. at random Find the probability that at test least one will fail the fest

Answer 1

Find prob. of failing test is = 0.25 prob. of passing test is = 0.75 Transportor choose two lorries at randon, we have to ;) Both will fail the test. ii) exactly one will pass test here we use binomial dist? :.x - be the no. of passing fest. ... P=0.75 ,q=0.25, n=2 ) P(x=0) = n(spx qn-2 -26, (0.75) °(.252 To.06257 i) P(x-1) = 26, (0.75).(0.25) = 0.375.1 2) of 12 loggies parked outside transpost leste 14 would faul if tested. p=1-9, q= 4/12 = 0.33 ; P=0.67. ;) n=2 ; we have to find both will pass tot BOX= 2) = 2(2067] (0.339 - 10.44897 0=2 ; we have to find one will fail pex=1) = ?<, (0.67) (6.33= 0.22117

1) n=3 we have to tind 2 will pass" and I will tail the test. le PCX = 2 )= 36, (0.673360.33)' = 104444] ;) n=4: we have to find prob. that cat a lecast one will fail ic plx= 3) + P(x = 2 ) + P(x= 1)+ PIX=0) = 4(710.67160.33)' +(0-673 (0:33] + 4,60.67(0.333° +40 (0-673 (033) 0.3970 + 0.2933 + 0.0463+0.0119 0.7985