What are the chances of the lunchbox contents?

No, there's no chance of getting 5 legendary or rare dwellers in one box, because the cards are fixed into categories, then the chances are divided into what you will get of those categories:

You will get:

• A Caps Card - 100 (85%)/500 Caps (15%)
• A Resource Card* - 50 power/food/water/1 stimpak/1 radaway
• A Weapon/Outfit Card - Normal (85%)/Rare (10%)/Legendary (5%)
• "Guaranteed Rare" Card* - 500 Caps/Weapon(Rare - 70%; Legendary - 30%)/Outfit(Rare - 50%; Legendary - 50%)/Dweller(rare - 90%; Legendary - 10%)

^{*The chance of what type of card you will get is an equal chance}

For those keeping track at home, that means you could theoretically get two MIRVs out of a single lunchbox, although the chances are pretty astronomical. I think about 1 in 1.8 million

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