The probability that a candidate passes a certain professional examination is 0.7. Find the probability that a candidate would pass the examination before the fourth attempt.

1. The probability that a candidate passes a certain professional
examination is 0.7. Find the probability that a candidate would
pass the examination before the fourth attempt.
Solution
𝑷 = 𝑷𝒂𝒔𝒔𝒊𝒏𝒈 𝒑𝒓𝒐𝒃𝒂𝒃𝒊𝒍𝒊𝒕𝒚 = 𝟎. 𝟕
𝑷
̅ = 𝑵𝒐𝒕 𝒑𝒂𝒔𝒔𝒊𝒏𝒈 𝒑𝒓𝒐𝒃𝒂𝒃𝒊𝒍𝒊𝒕𝒚 = 𝟏 − 𝟎. 𝟕 = 𝟎. 𝟑
Let
A = Candidate would pass the examination before the fourth attempt.
𝑷(𝑨) = 𝑭𝒊𝒓𝒔𝒕 𝒂𝒕𝒕𝒆𝒎𝒑𝒕 𝒐𝒓 𝑺𝒆𝒄𝒐𝒏𝒅 𝒂𝒕𝒕𝒆𝒎𝒑𝒕 𝒐𝒓 𝒕𝒉𝒊𝒓𝒅 𝒂𝒕𝒕𝒆𝒎𝒑𝒕
𝑃(𝐴) = 𝑷 + 𝑷
̅𝑷 + 𝑷
̅𝑷
̅𝑷
𝑃(𝐴) = 𝟎.𝟕 + (𝟎.𝟑)(𝟎.𝟕) + (𝟎.𝟑)(𝟎.𝟑)(𝟎.𝟕)
𝑃(𝐴) == 𝟎.𝟗𝟕𝟑