Skip to content

Course home

Sign up

2 Statistics

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511
Question 337

A botanical research station analyzes 50 plant samples for the presence of three specific enzymes: Alpha (AAA), Beta (BBB), and Gamma (ΓΓΓ). The distribution of these enzymes across the samples is summarized in the following data:

  • 9 samples contain only enzyme AAA.
  • 6 samples contain both enzymes A A\,A and BBB, but not ΓΓΓ.
  • 11 samples contain only enzyme BBB.
  • 4 samples contain both enzymes B B\,B and ΓΓΓ, but not AAA.
  • 8 samples contain only enzyme ΓΓΓ.
  • 12 samples contain none of these enzymes.
  • No samples contain both A A\,A and Γ Γ\,Γ simultaneously.

One sample is selected at random.

a.

Show that the probability that the sample contains more than one enzyme is 0.2.

[2]
b.

Determine the probability that the sample contains enzyme A A\,A or enzyme BBB (or both).

[2]
c.

State the probability that the sample contains both enzyme A A\,A and enzyme ΓΓΓ.

[1]
d.

Given that the sample is found to contain at least one of the three enzymes,

calculate the probability that it contains enzyme ΓΓΓ.

[3]
e.

Determine, with a reason, whether the presence of enzyme B B\,B and the presence of enzyme Γ Γ\,Γ in a sample are statistically independent events.

[4]
Markscheme

2 Statistics Questions

  1. A Level
  2. /Maths
  3. /2 Statistics

Question bank